Short-term motor adaptation to novel movement dynamics has been shown to involve at least two concurrent learning processes: a slow process that responds weakly to error but retains information well and a fast process that responds strongly to error but has poor retention. This modeling framework can explain several properties of motion-dependent motor adaptation (e.g., 24 h retention). An important assumption of this computational framework is that learning is only based on the experienced movement error, and the effect of noise (either internally generated or externally applied) is not considered. We examined the respective error sensitivity by quantifying adaptation in three subject groups distinguished by the noise added to the motion-dependent perturbation. We assessed the feedforward adaptive changes in motor output and examined the adaptation rate, retention, and decay of learning. Applying a two-state modeling framework showed that the applied noise during training mainly affected the fast learning process, with the slow process largely unaffected; participants in the higher noise groups demonstrated a reduced force profile following training, but the decay rate across groups was similar, suggesting that the slow process was unimpaired across conditions. Collectively, our results provide evidence that noise significantly decreases motor adaptation, but this reduction may be due to its influence over specific learning mechanisms. Importantly, this may have implications for how the motor system compensates for random fluctuations, especially when affected by brain disorders that result in movement tremor (e.g., essential tremor).